Balancing polynomials and their derivatives

We study the generalization of balancing numbers with a new sequence of numbers called $k$-balancing numbers. Moreover,
by using the Binet formula for $k$-balancing numbers, we obtain the identities including the generating function of these
numbers. In addition, the properties of divisibility of these numbers are investigated. Further, balancing polynomials that
are natural extensions of the $k$-balancing numbers are introduced and some relations for the derivatives of these polynomials
in the form of convolution are also proved.